Geodesic
Reductions of Galois representations for slopes in $(1,2)$
Documenta mathematica, Tome 20 (2015), pp. 943-987
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We describe the semisimplifications of the mod p reductions of certain crystalline two-dimensional local Galois representations of slopes in (1,2) and all weights. The proof uses the compatibility between the p-adic and mod p Local Langlands Correspondences for GL2​(Qp​). We also give a complete description of the submodules generated by the second highest monomial in the mod p symmetric power representations of GL2​(Fp​).
DOI : 10.4171/dm/510
Classification : 11F80
Mots-clés : local Langlands correspondence, reductions of Galois representations, Hecke operators 
@article{10_4171_dm_510,
     author = {Shalini Bhattacharya and Eknath Ghate},
     title = {Reductions of {Galois} representations for slopes in $(1,2)$},
     journal = {Documenta mathematica},
     pages = {943--987},
     year = {2015},
     volume = {20},
     doi = {10.4171/dm/510},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/510/}
}
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Shalini Bhattacharya; Eknath Ghate. Reductions of Galois representations for slopes in $(1,2)$. Documenta mathematica, Tome 20 (2015), pp. 943-987. doi: 10.4171/dm/510

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